Journal of Function Spaces
http://www.hindawi.com
The latest articles from Hindawi Publishing Corporation
© 2015 , Hindawi Publishing Corporation . All rights reserved.

HyersUlam Stability of the FirstOrder Matrix Differential Equations
Mon, 30 Nov 2015 08:26:39 +0000
http://www.hindawi.com/journals/jfs/2015/614745/
We prove the generalized HyersUlam stability of the firstorder linear homogeneous matrix differential equations . Moreover, we apply this result to prove the generalized HyersUlam stability of the th order linear differential equations with variable coefficients.
SoonMo Jung
Copyright © 2015 SoonMo Jung. All rights reserved.

The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators
Wed, 25 Nov 2015 14:07:30 +0000
http://www.hindawi.com/journals/jfs/2015/823862/
Let be a Schrödinger operator acting on , , where is a nonnegative locally integrable function on . In this paper, we will first define molecules for weighted Hardy spaces associated with and establish their molecular characterizations. Then, by using the atomic decomposition and molecular characterization of , we will show that the imaginary power is bounded on for , and the fractional integral operator is bounded from to , where , , and .
Hua Wang
Copyright © 2015 Hua Wang. All rights reserved.

Lebesgue Decomposition Theorem and Weak RadonNikodým Theorem for Generalized Fuzzy Number Measures
Wed, 25 Nov 2015 05:34:17 +0000
http://www.hindawi.com/journals/jfs/2015/576134/
The Lebesgue type decomposition theorem and weak RadonNikodým theorem for fuzzy valued measures in separable Banach spaces are established.
CaiLi Zhou and FuGui Shi
Copyright © 2015 CaiLi Zhou and FuGui Shi. All rights reserved.

Necessary and Sufficient Conditions for Inner Functions to Be in Spaces
Tue, 24 Nov 2015 07:51:48 +0000
http://www.hindawi.com/journals/jfs/2015/376089/
Under some regularity conditions on , inner functions in spaces are characterized in the following way: an inner function belongs to if and only if it is a Blaschke product associated with satisfying , where . The result generalizes earlier theorems in (Essén et al., 2006) and (PérezGonzález and Rättyä, 2009).
Atte Reijonen
Copyright © 2015 Atte Reijonen. All rights reserved.

Topological Structures of Derivative Weighted Composition Operators on the Bergman Space
Wed, 18 Nov 2015 08:30:00 +0000
http://www.hindawi.com/journals/jfs/2015/672385/
We characterize the difference of derivative weighted composition operators on the Bergman space in the unit disk and determine when linearfractional derivative weighted composition operators belong to the same component of the space of derivative weighted composition operators on the Bergman space under the operator norm topology.
CeZhong Tong, Cheng Yuan, and ZeHua Zhou
Copyright © 2015 CeZhong Tong et al. All rights reserved.

Categories of Fuzzy Greedoids
Tue, 10 Nov 2015 07:34:07 +0000
http://www.hindawi.com/journals/jfs/2015/543247/
The concepts of greedoids, fuzzifying greedoids, and ()fuzzy greedoids are introduced and feasibility preserving mappings between greedoids are defined. Then feasibility preserving mappings, fuzzifying feasibility preserving mappings, and ()fuzzy feasibility preserving mappings are given as generalizations of feasibility preserving mappings. We study the relations among greedoids, greedoids, fuzzifying greedoids, and ()fuzzy greedoids from a categorical point of view.
ZhenYu Xiu and FuGui Shi
Copyright © 2015 ZhenYu Xiu and FuGui Shi. All rights reserved.

The Randomized American Option as a Classical Solution to the Penalized Problem
Tue, 27 Oct 2015 08:11:12 +0000
http://www.hindawi.com/journals/jfs/2015/245436/
We connect the exercisability randomized American option to the penalty method by showing that the randomized American option value is the unique classical solution to the Cauchy problem corresponding to the canonical penalty problem for American options. We also establish a uniform bound for , where is the infinitesimal generator of a geometric Brownian motion.
Guillaume Leduc
Copyright © 2015 Guillaume Leduc. All rights reserved.

Formulae for the Generalized Drazin Inverse of a Block Matrix in Banach Algebras
Wed, 21 Oct 2015 12:18:34 +0000
http://www.hindawi.com/journals/jfs/2015/767568/
We present some new representations for the generalized Drazin inverse of a block matrix in a Banach algebra under conditions weaker than those used in resent papers on the subject.
Xiaoji Liu and Xiaolan Qin
Copyright © 2015 Xiaoji Liu and Xiaolan Qin. All rights reserved.

Convergence Theorems for Generalized Functional Sequences of DiscreteTime Normal Martingales
Thu, 15 Oct 2015 12:13:34 +0000
http://www.hindawi.com/journals/jfs/2015/360679/
The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence
of generalized functional sequences of a discretetime normal martingale . A necessary and sufficient condition in terms of the Fock transform is obtained for such a sequence to be strongly convergent. A type of generalized martingales associated with is introduced and their convergence theorems are established.
Some applications are also shown.
Caishi Wang and Jinshu Chen
Copyright © 2015 Caishi Wang and Jinshu Chen. All rights reserved.

Recent Developments on Summability Theory and Its Applications
Wed, 07 Oct 2015 07:27:59 +0000
http://www.hindawi.com/journals/jfs/2015/934780/
Mikail Et, Mohammad Mursaleen, Syed Abdul Mohiuddine, Mahmut Işık, Jeff Connor, and Feyzi Başar
Copyright © 2015 Mikail Et et al. All rights reserved.

Unique Fixed Point Theorems for Generalized Contractive Mappings in Partial Metric Spaces
Mon, 05 Oct 2015 08:59:38 +0000
http://www.hindawi.com/journals/jfs/2015/960827/
We establish some unique fixed point theorems in complete partial metric spaces for generalized weakly contractive mappings, containing two altering distance functions under certain assumptions. Also, we discuss some examples in support of our main results.
Lakshmi Narayan Mishra, Shiv Kant Tiwari, Vishnu Narayan Mishra, and Idrees A. Khan
Copyright © 2015 Lakshmi Narayan Mishra et al. All rights reserved.

Performance on ICI SelfCancellation in FFTOFDM and DCTOFDM System
Mon, 05 Oct 2015 08:58:37 +0000
http://www.hindawi.com/journals/jfs/2015/854753/
In orthogonal frequency division multiplexing (OFDM) system, the existence of frequency offset in AWGN channel affects the orthogonality among the subcarriers and consequently introduces the intercarrier interference (ICI). The paper investigates new ICI selfcancellation technique to mitigate the effect of ICI in FFTOFDM and compares it to DCT based OFDM system in terms of bit error rate (BER) and carrier to interference ratio (CIR).
The proposed method for group size three results in a significant 20 dB improved CIR in FFTOFDM. In terms of BER, proposed ICI selfcancellation technique outperforms the other selfcancellation techniques in FFTOFDM. Also, this paper investigates outperforming BER and CIR improvement by using DCTOFDM without applying selfcancellation techniques, due to its energy compaction property.
Shilpi Gupta, Upena Dalal, and Vishnu Narayan Mishra
Copyright © 2015 Shilpi Gupta et al. All rights reserved.

On Uniform Convergence of Sequences and Series of FuzzyValued Functions
Sun, 04 Oct 2015 11:50:45 +0000
http://www.hindawi.com/journals/jfs/2015/870179/
The class of membership functions is restricted to trapezoidal one, as it is general enough and widely used. In the present paper since the utilization of Zadeh’s extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct for a fuzzyvalued function via related trapezoidal membership function. We derive uniform convergence of fuzzyvalued function sequences and series with some illustrated examples. Also we study Hukuhara differentiation and Henstock integration of a fuzzyvalued function with some necessary inclusions. Furthermore, we introduce the power series with fuzzy coefficients and define the radius of convergence of power series. Finally, by using the notions of Hdifferentiation and radius of convergence we examine the relationship between term by term Hdifferentiation and uniform convergence of fuzzyvalued function series.
Uğur Kadak and Hakan Efe
Copyright © 2015 Uğur Kadak and Hakan Efe. All rights reserved.

Stability of Pexiderized Quadratic Functional Equation in Random 2Normed Spaces
Thu, 01 Oct 2015 13:19:50 +0000
http://www.hindawi.com/journals/jfs/2015/828967/
The aim of this paper is to investigate the stability of HyersUlamRassias type theorems by considering the pexiderized quadratic functional equation in the setting of random 2normed spaces (RTNS), while the concept of random 2normed space has been recently studied by Goleţ (2005).
Mohammed A. Alghamdi
Copyright © 2015 Mohammed A. Alghamdi. All rights reserved.

UlamHyers Stability of Trigonometric Functional Equation with Involution
Thu, 01 Oct 2015 11:15:50 +0000
http://www.hindawi.com/journals/jfs/2015/742648/
Let and be a commutative semigroup and a commutative group, respectively, and the sets of complex numbers and nonnegative real numbers, respectively, and or an involution. In this paper, we first investigate general solutions of the functional equation for all , where . We then prove the HyersUlam stability of the functional equation; that is, we study the functional inequality for all , where and .
Jaeyoung Chung, ChangKwon Choi, and Jongjin Kim
Copyright © 2015 Jaeyoung Chung et al. All rights reserved.

Fourier Expansions with Polynomial Terms for Random Processes
Thu, 01 Oct 2015 08:40:49 +0000
http://www.hindawi.com/journals/jfs/2015/763075/
Based on calculus of random processes, we present a kind of Fourier expansions with simple polynomial terms via our decomposition method of random processes. Using our method, the expectations and variances of the corresponding coefficients decay fast and partial sum approximations attain the best approximation order. Moreover, since we remove boundary effect in our decomposition of random process, these coefficients can discover the instinct frequency information of this random process. Therefore, our method has an obvious advantage over traditional Fourier expansion. These results are also new for deterministic functions.
Zhihua Zhang
Copyright © 2015 Zhihua Zhang. All rights reserved.

On the Classical Paranormed Sequence Spaces and Related Duals over the NonNewtonian Complex Field
Thu, 01 Oct 2015 08:29:31 +0000
http://www.hindawi.com/journals/jfs/2015/416906/
The studies on sequence spaces were extended by using the notion of associated multiplier sequences. A multiplier sequence can be used to accelerate the convergence of the sequences in some spaces. In some sense, it can be viewed as a catalyst, which is used to accelerate the process of chemical reaction. Sometimes the associated multiplier sequence delays the rate of convergence of a sequence. In the present paper, the classical paranormed sequence spaces have been introduced and proved that the spaces are complete. By using the notion of multiplier sequence, the α, β, and γduals of certain paranormed spaces have been computed and their basis has been constructed.
Uğur Kadak, Murat Kirişci, and Ahmet Faruk Çakmak
Copyright © 2015 Uğur Kadak et al. All rights reserved.

Almost Statistical and Strongly Almost Convergence of
Order of Sequences of Fuzzy Numbers
Thu, 01 Oct 2015 08:27:37 +0000
http://www.hindawi.com/journals/jfs/2015/451050/
The main purpose of this article is to
introduce the concepts of almost statistical convergence and
strongly almost convergence of order of sequences of
fuzzy numbers with respect to an Orlicz function. We give some relations
between strongly almost convergence and almost statistical convergence of order of sequences of fuzzy numbers.
Mahmut Işık and Mikail Et
Copyright © 2015 Mahmut Işık and Mikail Et. All rights reserved.

The Characterization and Stability of gRiesz Frames for Super Hilbert Space
Wed, 30 Sep 2015 09:19:09 +0000
http://www.hindawi.com/journals/jfs/2015/465094/
Gframes and gRiesz frames as generalized frames in Hilbert spaces have been studied by many authors in recent years. The super Hilbert space has a certain advantage compared with the Hilbert space in the field of studying quantum mechanics. In this paper, for super Hilbert space , the definitions of a gRiesz frame and minimal gcomplete are put forward; also a characterization of gRiesz frames is obtained. In particular, we generalize them to general super Hilbert space . Finally, a conclusion of the stability of a gRiesz frame for the super Hilbert space is given.
Dingli Hua and Yongdong Huang
Copyright © 2015 Dingli Hua and Yongdong Huang. All rights reserved.

Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means
Mon, 28 Sep 2015 13:36:56 +0000
http://www.hindawi.com/journals/jfs/2015/452823/
We present the best possible parameters and such that double inequalities , hold for all with , where , and are the arithmetic, second contraharmonic, and Toader means of and , respectively.
WeiMao Qian, YingQing Song, XiaoHui Zhang, and YuMing Chu
Copyright © 2015 WeiMao Qian et al. All rights reserved.

Topological and Functional Properties of Some Algebras of Holomorphic Functions
Thu, 17 Sep 2015 13:35:41 +0000
http://www.hindawi.com/journals/jfs/2015/850709/
Let be the Privalov class of holomorphic functions on the open unit disk in the complex plane. The space equipped with the topology given by the metric defined by , , becomes an algebra. For each , we also consider the countably normed Fréchet algebra of holomorphic functions on which is the Fréchet envelope of the space . Notice that the spaces and have the same topological duals. In this paper, we give a characterization of bounded subsets of the spaces and weakly bounded subsets of the spaces with . If denotes the strong dual space of and denotes the space of complex sequences satisfying the condition , equipped with the topology of uniform convergence on weakly bounded subsets of , then we prove that both set theoretically and topologically. We prove that for each is a Montel space and that both spaces and are reflexive.
Romeo Meštrović
Copyright © 2015 Romeo Meštrović. All rights reserved.

Multiple Solutions for Kirchhoff Equations under the Partially Sublinear Case
Tue, 15 Sep 2015 09:53:33 +0000
http://www.hindawi.com/journals/jfs/2015/610858/
We prove the infinitely many solutions to a class of sublinear Kirchhoff type equations by using an extension of Clark’s theorem established by Zhaoli Liu and ZhiQiang Wang.
Wenjun Feng and Xiaojing Feng
Copyright © 2015 Wenjun Feng and Xiaojing Feng. All rights reserved.

Some Compactness and Interpolation Results for Linear Boltzmann Equation
Mon, 07 Sep 2015 14:20:43 +0000
http://www.hindawi.com/journals/jfs/2015/370294/
We discuss some compactness results in spaces related to the spectral theory of neutron transport equations for general classes of collision operators and Radon measures having velocity spaces as supports covering most physical models. We show in particular that the asymptotic spectrum of the transport operator is independent of .
Nadjeh Redjel and Abdelkader Dehici
Copyright © 2015 Nadjeh Redjel and Abdelkader Dehici. All rights reserved.

Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces
Wed, 02 Sep 2015 12:54:07 +0000
http://www.hindawi.com/journals/jfs/2015/420750/
We characterize the set of functions for which strong summability holds at each Lebesgue point. More exactly, if is in the Wiener amalgam space and is almost everywhere locally bounded, or , then strong summability holds at each Lebesgue point of . The analogous results are given for Fourier series, too.
Ferenc Weisz
Copyright © 2015 Ferenc Weisz. All rights reserved.

Shifting and Variational Properties for FourierFeynman Transform and Convolution
Tue, 01 Sep 2015 11:32:03 +0000
http://www.hindawi.com/journals/jfs/2015/580653/
Shifting, scaling, modulation, and variational properties for FourierFeynman transform of functionals in a Banach algebra are given. Cameron and Storvick's translation theorem can be obtained as a corollary of our result. We also study shifting, scaling, and modulation properties for the convolution product of functionals in .
Byoung Soo Kim
Copyright © 2015 Byoung Soo Kim. All rights reserved.

Weighted Weak Local Hardy Spaces Associated with Schrödinger Operators
Tue, 01 Sep 2015 06:28:38 +0000
http://www.hindawi.com/journals/jfs/2015/490259/
We characterize the weighted weak local Hardy spaces related to the critical radius function and weights which locally behave as Muckenhoupt’s weights and actually include them, by the atomic decomposition. As an application, we show that localized Riesz transforms are bounded on the weighted weak local Hardy spaces.
Hua Zhu
Copyright © 2015 Hua Zhu. All rights reserved.

ChoiDavisJensen Inequalities in Semifinite von Neumann Algebras
Mon, 31 Aug 2015 11:41:25 +0000
http://www.hindawi.com/journals/jfs/2015/208923/
We prove the ChoiDavisJensen type submajorization inequalities on semifinite von Neumann algebras for concave functions and convex functions.
Turdebek N. Bekjan, Kordan N. Ospanov, and Asilbek Zulkhazhav
Copyright © 2015 Turdebek N. Bekjan et al. All rights reserved.

On Approximate Controllability of SecondOrder Neutral Partial Stochastic Functional Integrodifferential Inclusions with Infinite Delay and Impulsive Effects
Sun, 30 Aug 2015 08:23:40 +0000
http://www.hindawi.com/journals/jfs/2015/925209/
We discuss the approximate controllability
of secondorder impulsive neutral partial stochastic functional
integrodifferential inclusions with infinite delay under the
assumptions that the corresponding linear system is approximately
controllable. Using the fixed point strategy, stochastic analysis,
and properties of the cosine family of bounded linear operators
combined with approximation techniques, a new set of sufficient
conditions for approximate controllability of the secondorder
impulsive partial stochastic integrodifferential systems are
formulated and proved. The results in this paper are generalization
and continuation of the recent results on this issue. An example is
provided to show the application of our result.
Zuomao Yan
Copyright © 2015 Zuomao Yan. All rights reserved.

Functions of Bounded th Variation and Continuity Modulus
Sun, 23 Aug 2015 09:32:14 +0000
http://www.hindawi.com/journals/jfs/2015/253636/
A scale of spaces exists connecting the class of functions of bounded th variation in the sense of RieszMerentes with the Sobolev space of functions with integrable th derivative. This scale is generated by the generalized functionals of Merentes type. We prove some limiting relations for these functionals as well as sharp estimates in terms of the fractional modulus of smoothness of order .
Odalis Mejía and Pilar Silvestre
Copyright © 2015 Odalis Mejía and Pilar Silvestre. All rights reserved.

Positive Solutions of TwoPoint Boundary Value Problems for MongeAmpère Equations
Thu, 20 Aug 2015 08:52:48 +0000
http://www.hindawi.com/journals/jfs/2015/620251/
This paper considers the following boundary value problem: , where is odd. We establish the method of lower and upper solutions for some boundary value problems which generalizes the above equations and using this method we present a necessary and sufficient condition for the existence of positive solutions to the above boundary value problem and some sufficient conditions for the existence of positive solutions.
Baoqiang Yan and Meng Zhang
Copyright © 2015 Baoqiang Yan and Meng Zhang. All rights reserved.